Chapter 11
Fundamentals of
Interest Rate
Futures
1
© 2004 South-Western Publishing
Summary



2
Reconcile expectation and Cost of Carry
hypothesis of pricing future contracts on
foreign exchange
Find forward exchange rate based on IRP and
PPP
Learn term structure of interest rates and its
use in pricing financial assets
Outline





3
Interest rate futures – yield curve
Treasury bills, eurodollars, and their futures
contracts
Discount yield vs. Investment Rate %”
(bond equivalent yield):
Pricing interest rate futures contracts
Spreading with interest rate futures
Interest Rate Futures

Exist across the yield curve and on many
different types of interest rates
– U.S. Treasury Bills
–
–
–
4
Eurodollar (ED) futures contracts
30-day Federal funds contracts
Other Treasury contracts
Characteristics of U.S. Treasury
Bills
5

Sell at a discount from par using a 360-day
year and twelve 30-day months

91-day (13-week) and 182-day (26-week) Tbills are sold at a weekly auction
Characteristics of U.S. Treasury
Bills (cont’d)
Treasury Bill Auction Results
6
Term
Issue Date
Auction
Date
Discount
Rate %
Investment
Rate %
Price Per
$100
13-week
01-02-2004
12-29-2003
0.885
0.901
99.779
26-week
01-02-2004
12-29-2003
0.995
1.016
99.500
4-week
12-26-2003
12-23-2003
0.870
0.882
99.935
13-week
12-26-2003
12-22-2003
0.870
0.884
99.783
26-week
12-26-2003
12-22-2003
0.970
0.992
99.512
4-week
12-18-2003
12-16-2003
0.830
0.850
99.935
Characteristics of U.S. Treasury
Bills (cont’d)

The “Discount Rate %” is the discount yield, calculated
as:
Discount Yield 
7
Par Value - Market Price
360

Par Value
Days
Characteristics of U.S. Treasury
Bills (cont’d)
Discount Yield Computation Example
For the first T-bill in the table on slide 6, the discount yield is:
Par Value - Market Price 360
Discount Yield 

Par Value
Days
10,000  9,977.90 360


 0.884%
10,000
90
8
Characteristics of U.S. Treasury
Bills (cont’d)

The discount yield relates the income to the
par value rather than to the price paid and
uses a 360-day year rather than a 365-day
year
–
Calculate the “Investment Rate %” (bond
equivalent yield):
Bond Equivalent Yield 
9
Discount Amount
365

Discount Price
Days to maturity
Characteristics of U.S. Treasury
Bills (cont’d)
Bond Equivalent Yield Computation Example
For the first T-bill in the table on slide 6, the bond equivalent
yield is:
Discount Amount
365
Bond Equivalent Yield 

Discount Price
Days to maturity
10,000  9,977.90 365


 0.90%
9,977.90
90
10
The Treasury Bill Futures
Contract

Treasury bill futures contracts call for the
delivery of $1 million par value of 91-day Tbills on the delivery date of the futures
contract
–
11
On the day the Treasury bills are delivered, they
mature in 91 days
The Treasury Bill Futures
Contract (cont’d)
Futures position
91-day T-bill
T-bill
established
delivered
matures
91 days
Time
12
The Treasury Bill Futures
Contract (cont’d)
T-Bill Futures Quotations
September 15, 2000
13
Open
High
Low
Settle
Change
Settle
Change
Open
Interest
Sept
94.03
94.03
94.02
94.02
-.01
5.98
+.01
1,311
Dec
94.00
94.00
93.96
93.97
-.02
6.03
+.02
1,083
Characteristics of Eurodollars


Applies to any U.S. dollar deposited in a
commercial bank outside the jurisdiction of
the U.S. Federal Reserve Board
Banks may prefer eurodollar deposits to
domestic deposits because:
–
–
14
They are not subject to reserve requirement
restrictions
Every ED received by a bank can be reinvested
somewhere else
The Eurodollar Futures Contract

The underlying asset with a eurodollar
futures contract is a three-month, $1 million
face value instrument
–
A non-transferable time deposit rather than a
security

15
The ED futures contract is cash settled with no actual
delivery
The Eurodollar Futures Contract
(cont’d)
Treasury Bill vs Eurodollar Futures
Treasury Bills
16
Eurodollars
Deliverable underlying commodity
Undeliverable underlying commodity
Settled by delivery
Settled by cash
Transferable
Non-transferable
Yield quoted on discount basis
Yield quoted on add-on basis
Maturities out to one year
Maturities out to 10 years
One tick is $25
One tick is $25
The Eurodollar Futures Contract
(cont’d)


The quoted yield with eurodollars is an addon yield
For a given discount, the add-on yield will
exceed the corresponding discount yield:
Discount
360
Add - on Yield 

Pr ice
Days to Maturity
17
The Eurodollar Futures Contract
(cont’d)
Add-On Yield Computation Example
An add-on yield of 1.24% corresponds to a discount of
$3,124.66:
Discount
360
Add - on Yield 

Pr ice
Days to Maturity
Discount
360
.0124 

$1,000,000  Discount 91
Discount  $3,124.66
18
The Eurodollar Futures Contract
(cont’d)
Add-On Yield Computation Example (cont’d)
If a $1 million Treasury bill sold for a discount of $3,124.66 we
would determine a discount yield of 1.236%:
$3,124.66 360
Discount Yield 

 1.236%
$1,000,000 91
19
Speculating With Eurodollar
Futures
20

The price of a fixed income security moves
inversely with market interest rates

Industry practice is to compute futures
price changes by using 90 days until
expiration
Hedging With Eurodollar Futures

21
Using the futures market, hedgers can lock
in the current interest rate
Hedging With Eurodollar
Futures (cont’d)
Hedging Example
Assume you are a portfolio managers for a university’s
endowment fund which will receive $10 million in 3 months.
You would like to invest the money now, as you think interest
rates are going to decline. Because you want a money market
investment, you establish a long hedge in eurodollar futures.
Using the figures from the earlier example, you are promising
to pay $993,150.00 for $1 million in eurodollars if you buy a
futures contract at 98.76. Using the $10 million figure, you
decide to buy 10 MAR ED futures, promising to pay
$9,969,000.
22
Hedging With Eurodollar
Futures (cont’d)
Hedging Example (cont’d)
When you receive the $10 million in three months, assume
interest rate have fallen to 1.00%. $10 million in T-bills would
then cost:
 .01 90 
Price  $10,000,0001 
 $9,975,000.00

360 

This is $6,000 more than the price at the time you established
the hedge.
23
Hedging With Eurodollar
Futures (cont’d)
Hedging Example (cont’d)
In the futures market, you have a gain that will offset the
increased purchase price. When you close out the futures
positions, you will sell your contracts for $6,000 more than
you paid for them.
24
Characteristics of U.S. Treasury
Bonds

Very similar to corporate bonds:
–
–
–

Different from Treasury notes:
–
–
25
Pay semiannual interest
Have a maturity of up to 30 years
Are readily traded in the capital markets
Notes have a life of less than ten years
Some T-bonds may be callable fifteen years after
issuance
Characteristics of U.S. Treasury
Bonds (cont’d)

Bonds are identified by:
–
–
–
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26
The issuer
The coupon
The year of maturity
E.g., “U.S. government six and a quarters of
23” means Treasury bonds with a 6¼%
coupon rate that mature in 2023
Pricing of Treasury Bonds

To find the price of a bond, discount the
cash flows of the bond at the appropriate
spot rates:
Ct
P0  
t
t 1 (1  Rt )
N
27
Pricing of Treasury Bonds
(cont’d)
Bond Pricing Example
Suppose we have a government bond with one year
remaining to maturity and a coupon rate of 6%. 6-months
spot rates are 5.73% and 12 months spot rates are 5.80%.
What is the price of the bond?
28
Pricing of Treasury Bonds
(cont’d)
Bond Pricing Example (cont’d)
$30
$1,030
P0 

 $1,002.71
0.5
1.0
(1.0573)
(1.0580)
This corresponds to a newspaper price of about 100 8/32nds.
29
Pricing of Treasury Bonds
(cont’d)
Bond Pricing Example (cont’d)
To solve for the yield to maturity, we can either look
at a “bond book,” use a spreadsheet package, or
use a financial calculator. The yield to maturity in
this example is 5.72%.
30
Dealing With Coupon
Differences

31
To standardize the $100,000 face value
Tbond contract traded on the Chicago Board
of Trade, a conversion factor is used to
convert all deliverable bonds to bonds
yielding 6%
The Matter of Accrued Interest

The Treasury only mails interest payment
checks twice a year, but bondholders earn
interest each calendar day they hold a bond

When someone buys a bond, they pay the
accrued interest to the seller of the bond
–
32
Calculated using a 365-day year
Cheapest to Deliver
33

Normally, only one bond eligible for delivery
will be cheapest to deliver

A hedger will collect information on all the
deliverable bonds and select the one most
advantageous to deliver
Pricing Interest Rate Futures
Contracts

Interest rate futures prices come from the
implications of cost of carry:
Ft  S (1  C0,t )
where
Ft  futures price for delivery at time t
C0 , t
34
S  spot commodity price
 cost of carry from time zero to time t
Computation

Cost of carry is the net cost of carrying the
commodity forward in time (the carry return
minus the carry charges)
–

35
If you can borrow money at the same rate that a
Treasury bond pays, your cost of carry is zero
Solving for C in the futures pricing equation
yields the implied repo rate (implied
financing rate)
Arbitrage With T-Bill Futures

If an arbitrageur can discover a disparity between
the implied financing rate and the available repo
rate, there is an opportunity for riskless profit
–
–
36
If the implied financing rate is greater than the
borrowing rate, then he/she could borrow, buy Tbills, and sell futures
If the implied financing rate is lower than the
borrowing rate, he/she could borrow, buy T-bills,
and buy futures
Spreading With Interest Rate
Futures

TED spread Involves the T-bill futures
contract and the eurodollar futures contract
37
Maturity Spread
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38
NOB spread ( change of slope)
Summary
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39
Discount vs. investment (bond, add-on) yield
Bond pricing (new based on yield curve)
Pricing of Interest rate future and Arbitrage
Spreading Interest rate futures